Because we want to edit parts of the sprite, and not all of it, we'll first separate the parts we want to edit from the rest. Before we do anything else, we'll move a copy of the important parts into another layer. The important parts are everything but the background and the shadow, so we will choose those two and then inverse the selection, leaving us with just the Seraph. To do this, choose either the wand or the color selection tool. They are good for selecting large areas of even color. Use the tool to first select the whole white background, then hold Shift and add the whole black shadow to the selection. Now right-click on the image window, and from the menu that appears choose Selection - Inverse.
Next, we'll copy the seraph into a new layer. Choose the layer window, and from its bottom-left corner, choose New Layer. You don't have to name it or anything, just make sure it's Transparent, not filled with color (primary, secondary or white). Now you should have two layers visible in the layers window. You can drag one to change their order, or click on the eye icon to hide one or both of them. You must also ALWAYS select which layer you are working on. Click on the first layer, named "background" or something similar, and copy the seraph sprite (Ctrl-C, or Edit - Copy). Now choose the new layer, and paste the sprite (Ctrl-V). (You can move this "floating layer" that has the pasted sprite in it around before you lock it in place. You can move it around when you choose the mover tool (four arrows form a cross) or one of the selector tools. You lock it in place by clicking inside the selection if using the mover tool, or outside of it if using a selection tool. You'll see a small anchor next to your mouse when a single click would lock it in place. However, in this case you don't want to move the sprite.)
Now we can start changing the colors. Right-click on the image window, and from the menu choose Layer (in the middle) - Colors - and then one of the first three tools. They all can be used to cause various interesting effects. Experiment. You'll see the wings, hands and legs turn into various strange colors, but don't care about that. The fourth tool, used to change birghtness and contrast, is useful for bringing out the colors a bit better, and to e.g. change reddish-orange bird into a blazing red-yellow phoenix. I used the second tool (HLS) with settings 157 for Hue, -62 for L (light?) and 100 for S (saturation?), and the fourth to increase contrast a bit and to adjust brightness so that the new contrast values look good.
Now we have all the parts we need for the final sprite. You can use the eraser tool to get rid of the unwanted parts in the second layer, or use one of the selector tools and cut (Ctrl-x) them out. I've found that the latter is easier to use, but YMMV. You can also make a new layer, and copy the wings, legs and hands of the original sprite into that one. I did that. I used color chooser to first select the skin area, and changed the tool options and the pixel I selected until I got the both hands and feet selected. Then I used Shift to add parts of the wings to the selection, undoing all selections that started selected parts of the robe. It took several minor selections to get most of the wings, and the few parts left I took with the rectangular selection tool. I copied these parts into a new layer.
The dagger still looked funny, so I copied the dagger from the original sprite, copied it into a new layer and adjusted it until it was bright yellow. Then I added few bright red dots with the pen, on 40% transparency, an the same spots the original had dots of darker blue. This gave the dagger orangish blade.
When you want to save the image, remember that writing the file of the name as "redseraph.tga" is enough. Gimp understands that you want to save a targa file from that. You don't have to choose the filetype from the filetype browser, although you can if you want.
This image shows the three parts that form the final image, and the final image. The leftmost is the original layer, which is actually the only one that has the black background and the magenta shadow. The one next to it is the color-edited seraph, whose wings and hands are replaced by the third image. The last sprite of the jpg is the final one, with the dagger also changed. I left the dagger layer out.